Estimate how many values fall below a specific deviation using the empirical rule I'm trying to estimate how many values fall within a portion of the standard deviation
Lets say I have:
A sample size of 100
and Average of 50.
and a start deviation of 10.

Using the Empirical Rule we can say that ~34 of the values should be between 50-60
But what if I wanted to determine how many values are between 50-55?
Since this is a curve I know the data is not linear so 34/2 is not the answer.
How can I calculate how many values fall within a fraction of a deviation?
Note: I do not fully understand mathematical symbols so please explain the algorithm in english instead.
 A: You're correct that the "empirical rule" that you've presented isn't sufficient to answer the question, because the interval $(50, 55]$ isn't illustrated on the diagram.
But the empirical rule is just a more specific statement about a very general fact about CDFs. For every distribution, cumulative distribution function is defined as $F_X(x) = \mathbb{P}(X \le x)$. If you want to know the probability that a sample is in an interval $(a,b]$, then you can use the difference of CDFs: $$\mathbb{P}(X \in (a,b])=F_X(b) - F_X(a).$$ This fact is important because it's true for any probability distribution, for any interval. In the special case that $F_X$ is a standard normal CDF, then we can show that the empirical rule that you've presented just reproduces this identity.
For $\mu=50, \sigma=10$, we have $$\mathbb{P}(X \in (50,55])\approx 0.1914625 = p$$
In a random sample of 100 values, all we know for sure is that the number of values $Y$ in the interval $(50, 55]$ can be 0, 1, 2, ... or 100. But not all of these cases have the same probability. Assuming that the data are drawn independently from this normal distribution, then we know that
$$Y \sim \text{Binom}(100, p)$$
and this distribution looks like this.

On average, there will be $100p\approx 19.14625$ samples in $(50,55]$.
A: I've found a way to get the answer I was looking for.  I don't know much math or math terms so I'll try to explain it the way I was told/understand it
For a normal distribution, the percentage of values falling within k⋅σ of the mean is given by erf(k/sqrt(2)) where erf is the error function. For example, erf(1/sqrt(2)) = 0.682689.. and erf(3/sqrt(2)) = 0.997300...
To summarize:  If you want to get the estimated number of samples between 50 (the mean) and 55.
We can calulate the fraction of the deviation that we want in this case
The portion we wanted to calculate was between the mean and 55.  Meaning the value deviated by 5
Deviation was 10.
we're trying to calculate (5/10) or 1/2 a deviation.  so if we call
erf(.5/sqrt(2))/2 we will get the answer were looking for.
